A223633 - OEIS

%I #8 Aug 22 2018 02:01:59

%S 11,121,801,3712,13599,42109,114713,282273,639165,1350228,2689169,

%T 5091414,9224755,16081503,27096217,44293439,70470225,109418622,

%U 166193601,247432316,361730919,520085521,736404249,1028097709,1416755525

%N Number of n X 4 0..1 arrays with rows, antidiagonals and columns unimodal.

%C Column 4 of A223637.

%H R. H. Hardin, <a href="/A223633/b223633.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/112)*n^8 - (1/72)*n^7 + (203/360)*n^6 + (37/360)*n^5 + (41/144)*n^4 + (901/36)*n^3 - (168481/2520)*n^2 + (5693/60)*n - 45 for n>2.

%F Conjectures from _Colin Barker_, Aug 21 2018: (Start)

%F G.f.: x*(11 + 22*x + 108*x^2 - 65*x^3 + 249*x^4 - 74*x^5 + 92*x^6 + 18*x^7 + 9*x^8 - 11*x^9 + x^10) / (1 - x)^9.

%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>11.

%F (End)

%e Some solutions for n=4:

%e ..0..0..1..0....0..1..1..0....1..0..0..0....0..0..0..1....0..1..0..0

%e ..0..1..1..1....0..1..1..0....1..0..0..0....0..1..1..0....0..1..1..0

%e ..1..1..1..1....0..1..1..0....1..1..0..0....1..1..1..0....0..0..0..1

%e ..1..0..0..0....1..1..1..1....0..1..1..0....0..1..0..0....0..0..0..1

%Y Cf. A223637.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 24 2013